This document discusses the modeling of the Diffie-Hellman key exchange algorithm using object-oriented analysis and design techniques, highlighting its application in securing communications. It details the algorithm's structure, implementation in C++, and offers a conceptual framework alongside various UML diagrams. The study concludes that object-oriented modeling effectively represents cryptosystems and their functionalities.

1. International Journal on Cryptography and Information Security (IJCIS), Vol. 14, No.2, June 2024
DOI:10.5121/ijcis.2024.14201 1
MODELING DIFFIE HELLMAN KEY EXCHANGE
ALGORITHM USING OBJECT-ORIENTED ANALYSIS
AND DESIGN TECHNIQUE
Ashioba, Nwanze Chukwudi1
, Emma-Osiebe Obaro2
, Ogbodhu, Charles Uzoma-
Odoji-Kpasa3
, Ndubuife Nonso Daniel4
1
Dennis Osadebay University AnwaiAsaba, Delta State, Nigeria
2
Delta State polytechnic Ogwashi-uku, Delta State, Nigeria
3
Michael & Cecilia Ibru University, Delta State, Nigeria
4
National Open University of Nigeria.
ABSTRACT
In a communicating system, information transmitted from one location (sender) to another (receiver) is
secured or protected from unauthorized users or intruders. Many cryptographic algorithms have been used
to prevent and protect data and information from being hacked by intruders. Both symmetric and
asymmetric algorithms have not been successful in simulating cryptosystems as real-world issues with
things enclosed in properties and procedures. This research simulates the Diffie Hellman key exchange
algorithm using object-oriented analysis and design techniques. The researchers used the Unified
Modeling Language tools in the analysis and design of the system and implemented the Diffie Hellman key
exchange algorithm using C++ object-oriented programming language. The outcome demonstrates that
cryptosystems are actual issues with entities having encapsulated properties and functions.
KEYWORDS
Asymmetric cryptography, Cryptography, public key, private key and symmetric cryptography
1. INTRODUCTION
Data and information in a communication system are always exposed to risks and attackers when
transmitted from one location to another. The security of these data and information can be
achieved by different cryptographic algorithms. [1] described cryptography as a method for
verifying the integrity and confidentiality of data in a communication system. Cryptography was
derived from the Greek origin “kryptos” meaning hidden and “graphy” meaning written word[2].
It is a technical method of encoding messages to prevent hackers from reading them.
Cryptography is a scientific method of altering information to prevent attacks[3]. In general
terms, cryptography is the technique and method of data encryption to avoid intrusion across
unreliable communication routes [4], [5]. It mainly uses the mathematical principle that generates
various algorithms called cryptographic algorithms [6]. To encrypt and decrypt information, a
mathematical function known as a cryptographic algorithm, or cipher is used. The algorithm and
a key are used to encrypt the plaintext [7]. In this context, cryptosystem refers to the collection of
cryptographic techniques and the key control procedure that permits the usage of the algorithms
in each application setting [7]. The two kinds of cryptographic techniques are symmetric and
public key [8], [9]. In symmetric cryptography, also known as classical cryptography, the
communicating parties share the same encoding/decoding key [8].Thus, the communicating
parties need to agree on a unique key before utilizing a symmetric key cryptographic technique.

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For symmetric key cryptography to function properly, both the sender and the recipient of the
communications must be aware of and employ the same secret key when communicating [9]. The
architecture of the symmetric cryptography is depicted in Figure 1.
Figure 1: Symmetric key cryptography
Establishing a consensus on a single secret key that only the people involved know is the
challenge with symmetric key cryptography. In 1977, Whitefield Diffie and Martin Hellman
released an article proposing a key exchange system as a solution to this issue, offering the first
workable solution. With the Diffie-Hellman key exchange protocol—named after them—two
parties can converse over an open channel and ascertain a shared secret key without exchanging
any secret keying information beforehand [9].
In asymmetric key cryptography or cryptosystems, different keys are utilised for encryption and
decoding [8].
Figure 2 depicts the asymmetric key cryptosystem.
Figure 2: Structure of Asymmetric encryption scheme
The keys in this case are related to one another mathematically. The asymmetric key
cryptosystem, sometimes referred to as the public key cryptosystem, encrypts and decrypts

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information using both private and public keys. Each user's public key is kept secret by
maintaining the confidential nature of their private key, which stops the communication parties
from exchanging or revealing sensitive data (keys). Because they offer the advantages of
confidentiality and authentication, public key cryptosystems are the most widely used.
2. DIFFIE-HELLMAN KEY EXCHANGE
The Diffie-Hellman key exchange, often known as the exponential key exchange, is a method for
securely sending cryptographic keys across an erratic channel. It is acrucial component of
several secure communication protocols, such as SSH, TLS, and SSL. A breakthrough in public
key cryptography was the Diffie-Hellman key exchange, which allows two parties to securely
generate a secret key for communication security. Diffie-Hellman protocols for authenticated key
exchange were developed by [10]. The protocol established a shared secret key for a group of
players, ensuring multicast integrity. Over time, numerous schemes have been proposed. [11]
designed a Diffie-Hellman-MAC key exchange system that functions efficiently using the keyed
MAC hash function. [12] created a redesigned internet architecture that decreased the likelihood
of covert network attacks. They strengthened the security of the encryption protocol by
enhancing the existing algorithm with additional security codes. [13] developed an advancement
in the Diffie-Hellman Algorithm. They applied certain mathematical algorithms to make the
communication secure. [14] developed a version of the Diffie-Hellman key exchange that secures
communication networks by utilizing the Blowfish encryption method.
Algorithm of the Diffie-Hellman Key Exchange
The algorithm of the Diffie-Hellman key exchangestates sequentially the step-by-step procedures
to generating the common secret key in a cryptographic system.
The steps include;
(1)Both parties agree on p and q, two positive numbers, where q is a group generator and p is
a positive prime number.
(2)Both parties randomly choose their private keys, say x and y respectively
(3)Both parties calculate their public keys
Ka = qx
mod p and Kb = qy
mod p
(4)Both parties exchange their public keys to compute the common shared key
Kab = qxy
mod p
3. CONCEPTUAL FRAMEWORK OF THE NEW SYSTEM
Figure 3 illustrates the conceptual framework of the Diffie-Hellman key exchange method. It
consists of two parties, each with their own private and public key. While the public key is shared
by all participants in the communication system, the private keys are kept confidential.

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Figure 3: Conceptual design of the Diffie-Hellman Key Exchange Algorithm
4. OBJECT-ORIENTED DESIGN PROCESS MODEL
[15] described the software engineering method known as the Object-Oriented Analysis and
Design (OOAD) model, which shows an architecture as a collection of interrelated entities
working together to address a specific problem.
Each entity in the object-oriented paradigm represents a set of real-world entities connected by
methods and properties. Classes including data and methods are developed in object-oriented
models, along with the methods needed to manipulate the data. Unified Modeling Language
designs for object-oriented model picture system.
The Unified Modeling Language is a graphical language utilised to define, construct, picture, and
document software system components. The use-case, class, sequence, and activity diagrams are
among the artifacts that the researchers employed in the present paper.
5. ANALYSIS OF THE DIFFIE-HELLMAN ALGORITHM USING A USE-CASE
DIAGRAM
5.1. Use-Case Diagram of the Diffie-Hellman Algorithm
The use case diagram shows a system's functionality from the perspective of an outside observer
[16]. It is a systematic method of acquiring data regarding the needs of a system as seen by its
users. Use cases, relationships, and actors make up its three main parts. To accomplish the user's
goal, an actor interacts with the system's use cases. Figure 4 shows the use-case diagram of the
Diffie-Hellman key exchange algorithm.

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Figure 4: Use-case diagram of the Diffie-Hellman Key Exchange
5.2. Diffie-Hellman Key Exchange Activity Diagram
An activity diagram represents the way controls are transferred from one task to another. It shows
a series of operations that are performed on part of classes in the system. Figure 5 shows the
activity diagram of the Diffie-Hellman key exchange algorithm.
Figure 5: Activity diagram of the Diffie-Hellman key exchange
5.3. Sequence Diagram of the Diffie-Hellman Key Exchange
A sequence diagram is a diagram that shows the interactions between different objects in a
sequential order. It represents the flow of messages from one object to another. The main

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objective of a sequence diagram is to represent how messages are exchanged between objects.
Figure 6 displays the Diffie-Hellman key exchange cryptosystem's sequence diagram.
Figure 6: Sequence diagram of the proposed cryptosystem
6. DIFFIE-HELLMAN KEY EXCHANGE DESIGN USING CLASS DIAGRAM
A class diagram is a rigid framework that illustrates the classes, properties, methods, and
interactions between the classes in a cryptosystem to describe its framework. Class names,
attributes, and methods are the three sections that make up a class in class diagrams. Class
diagrams also use concepts like inheritance, association, multiplicity, and visibility. The class
diagram for the proposed Diffie-Hellman key exchange algorithm is depicted in Figure 7.
Figure 7: Diffie-Hellman key exchange class diagram

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The class diagram, in Figure 8, has three classes (DHKE), sender and receiver. Both transmitter
and receiver classes in the class diagram are offspring of the parent class (DHKE), and they
acquire the methods and properties of their parent class (DHKE).
7. IMPLEMENTATION
Object-oriented programming languages have implemented the Diffie Hellman key exchange
algorithm. The programming language C++ was employed in this work. The researchers put the
three classes to the test during the implementation phase. Sender, Receiver, and Cryptosystem
constitute the classes. As the offspring of the cryptosystem (DHKE), the sender and recipient
acquire the attributes and functions of the cryptosystem. They implemented the Diffie Hellman
key exchange algorithm using C++ object-oriented programming language.
8. CONCLUSION
The study has demonstrated that object-oriented modeling techniques can be used to explain the
Diffie-Hellman key exchange algorithm. The modeling technique enabled communicating parties
in a cryptosystem to act like real-world things with encapsulated attributes and methods.
ACKNOWLEDGMENT
We would like to express our gratitude to our friends and families for their moral and financial
assistance in getting this work published.
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